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International Journal of Modern Physics B, ISSN 0217-9792, 07/2006, Volume 20, Issue 18, pp. 2561 - 2568
The present work constitutes a guided tour through the mathematics needed for a proper understanding of homotopy perturbation method as applied to various... 
Nonlinear equations | Homotopy perturbation method | Asymptotic solution | Constant expansion
Journal Article
International Communications in Heat and Mass Transfer, ISSN 0735-1933, 03/2006, Volume 33, Issue 3, pp. 391 - 400
One of the newest analytical methods to solve the nonlinear heat transfer equations is using both homotopy and perturbation methods in equations. Here,... 
Nonlinear equations | Radiation equation | Heat transfer | Homotopy–perturbation | Homotopy-perturbation | nonlinear equations | MECHANICS | THERMODYNAMICS | homotopy-perturbation | radiation equation | APPROXIMATE SOLUTION | heat transfer | Mechanical engineering | Analysis | Methods | Radiation
Journal Article
Journal of Low Frequency Noise, Vibration and Active Control, ISSN 1461-3484, 12/2019, Volume 38, Issue 3-4, pp. 1399 - 1403
The enhanced perturbation method is used to improve a governing equation to a higher order, followed by the classic perturbation method. This paper adopts the... 
periodic solution | Homotopy perturbation method | Duffing equation | frequency–amplitude relation | ACOUSTICS | frequency-amplitude relation | Viscosity | Duffing oscillators | Perturbation methods | Extreme values
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 04/2011, Volume 61, Issue 8, pp. 1963 - 1967
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations. This method is... 
Laplace transform method | Homotopy perturbation method | He's polynomials | Nonlinear advection equations | VARIATIONAL ITERATION METHOD | MATHEMATICS, APPLIED | Analysis | Methods | Algorithms
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2004, Volume 156, Issue 3, pp. 591 - 596
In the paper, an heuristical example is given to illustrate the basic idea of the homotopy perturbation method, so that homotopy perturbation method has made... 
Asymptotic method | Perturbation method | Homotopy | MATHEMATICS, APPLIED | STRONGLY NONLINEAR OSCILLATIONS | asymptotic method | homotopy | perturbation method | EXPANSION
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2004, Volume 156, Issue 2, pp. 527 - 539
Journal Article
Annals of Physics, ISSN 0003-4916, 10/2019, Volume 409, p. 167918
We obtain a mass function solving the Tolman–Oppenheimer–Volkoff (TOV) equation for isotropic and spherically symmetric system via homotopy perturbation method... 
Neutron star | Homotopy perturbation method | Equation of state | General relativity | EQUATION-OF-STATE | PHYSICS, MULTIDISCIPLINARY | SPHERES | MASS | RADIUS DETERMINATION
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2005, Volume 169, Issue 2, pp. 1186 - 1194
In this paper, we show that the so-called “homotopy perturbation method” is only a special case of the homotopy analysis method. Both methods are in principle... 
Nonlinear | Homotopy | Analytic solution | MATHEMATICS, APPLIED | nonlinear | OLDROYD 6-CONSTANT FLUID | homotopy | FLOW | analytic solution
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2004, Volume 151, Issue 1, pp. 287 - 292
In the paper, the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities. Only one iteration leads to high accuracy of the... 
Nonlinear oscillator | Homotopy perturbation method | MATHEMATICS, APPLIED | homotopy perturbation method | LINDSTEDT-POINCARE METHODS | nonlinear oscillator | EXPANSION | PARAMETER
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2003, Volume 135, Issue 1, pp. 73 - 79
In this paper, a new perturbation method is proposed. In contrast to the traditional perturbation methods, this technique does not require a small parameter in... 
Nonlinearity | Duffing equation | Perturbation methods | Homotopy | MATHEMATICS, APPLIED | APPROXIMATE SOLUTION | homotopy | nonlinearity | perturbation methods | duffing equation
Journal Article
Results in Physics, ISSN 2211-3797, 09/2018, Volume 10, pp. 270 - 271
•Homotopy perturbation method is a powerful tool to nonlinear oscillators.•A nonlinear oscillator with negative linear term is studied.•The negative... 
Nonlinear oscillator | Parameter expansion method | Homotopy perturbation method | PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | PARAMETER-EXPANDING METHOD | FLOW | NANOFLUID
Journal Article
Physics Letters A, ISSN 0375-9601, 2007, Volume 369, Issue 1, pp. 70 - 76
A new scheme, deduced from He's homotopy perturbation method, is presented for solving Lane–Emden type singular IVPs problem. The scheme is shown to be highly... 
Singular IVPs | Lane–Emden equation | He's homotopy perturbation method | Lane-Emden equation | singular IVPs | PHYSICS, MULTIDISCIPLINARY | ALGORITHM | DIFFERENTIAL-EQUATIONS | OSCILLATOR
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 61, Issue 2, pp. 250 - 254
Journal Article
Mathematical and Computer Modelling, ISSN 0895-7177, 2008, Volume 48, Issue 3, pp. 486 - 498
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 01/2017, Volume 41, pp. 180 - 194
•A modified Laplace transform homotopy perturbation method (MLT–HPM) is presented.•MLT–HPM improves the accuracy of approximate solutions obtained by other... 
Laplace transform | Homotopy perturbation method | Differential equations | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | HEAT-TRANSFER | HES POLYNOMIALS | EQUATION | FLOW | Engineering schools | Physical instruments | Analysis | Methods
Journal Article
by He, JH
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, ISSN 1230-3429, 06/2008, Volume 31, Issue 2, pp. 205 - 209
The homotopy perturbation method is extremely accessible to non-mathematicians and engineers. The method decomposes a complex problem under study into a series... 
RELATIVISTIC (AN)HARMONIC OSCILLATOR | EQUATIONS | STRONGLY NONLINEAR OSCILLATORS | FLOW | MATHEMATICS | nonlinear equations | homotopy perturbation | APPROXIMATE | FLUID | EXPANSION | PARAMETER-EXPANDING METHOD | SYSTEMS | KDV
Journal Article
International Journal of Nonlinear Sciences and Numerical Simulation, ISSN 1565-1339, 2005, Volume 6, Issue 2, pp. 207 - 208
Journal Article
by He, J H and He, J H
Indian Journal of Physics, ISSN 0973-1458, 2/2014, Volume 88, Issue 2, pp. 193 - 196
A homotopy perturbation method with two expanding parameters is suggested. The method is especially effective for a nonlinear equation with two nonlinear... 
Homotopy perturbation method | Physics, general | Duffing equation | Astrophysics and Astroparticles | Periodic solution | Physics | ELEMENTARY INTRODUCTION | PHYSICS, MULTIDISCIPLINARY | ASYMPTOTIC METHODS | Parameter estimation | Nonlinear equations
Journal Article
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